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Properties

Label 1848.2.ek
Level $1848$
Weight $2$
Character orbit 1848.ek
Rep. character $\chi_{1848}(115,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1536$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1848.ek (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 616 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1848, [\chi])\).

Total New Old
Modular forms 3136 1536 1600
Cusp forms 3008 1536 1472
Eisenstein series 128 0 128

Trace form

\( 1536 q + 4 q^{2} + 4 q^{4} - 8 q^{8} - 192 q^{9} + O(q^{10}) \) \( 1536 q + 4 q^{2} + 4 q^{4} - 8 q^{8} - 192 q^{9} - 8 q^{11} + 16 q^{14} - 4 q^{16} + 6 q^{18} - 40 q^{22} - 54 q^{24} + 192 q^{25} - 12 q^{28} - 16 q^{32} + 8 q^{36} + 12 q^{42} + 32 q^{43} + 54 q^{44} - 46 q^{46} - 56 q^{50} + 36 q^{52} + 64 q^{56} + 22 q^{58} + 96 q^{59} + 12 q^{60} - 32 q^{64} + 36 q^{66} + 16 q^{67} - 132 q^{68} + 64 q^{70} + 6 q^{72} + 68 q^{74} - 120 q^{78} + 192 q^{81} + 72 q^{82} - 60 q^{84} + 70 q^{86} + 2 q^{88} + 40 q^{91} - 188 q^{92} + 36 q^{94} - 288 q^{98} + 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1848, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1848, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1848, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(616, [\chi])\)\(^{\oplus 2}\)